Modern Graph Theory

Out of this list, the books I am familiar with, are great (Hilbert-Courant, Spivak, Korner's books). At the same time, even with extensive mathematical training, I haven't read them from start to finish. I wouldn't even like to say "read". For someone who's not used to mathematical reading, some of these books require careful study. That means generating examples to understand results (theorems), trying your own conjectures, proving things yourself etc. Over time, one becomes familiar with most/all the material in a book but the knowledge might have been acquired through various books (and courses) over time. Also, mathematics is a massive field. The first question would be what kinds of mathematics would you like to get better at. There are great books in analysis. If you are starting out with a solid calculus knowledge, try Abbott's Understanding Analysis [1] or Duren's Invitation to Classical Analysis [2]. For asymptotic methods in PDEs, try Bender and Orszag [3] which is a wonderful book. But again, this might not be your cup of tea at all and there are more abstract or formal books like Rudin's.…

I don't think there is a definitive answer for your question because computer science is a relative new area of knowledge and “fundamental books” are still being published. If I had to say one text that is the fundamental one, I would go with a paper: “On Computable Numbers, with an Application to the Entscheidungsproblem” [1], by Alan Turing. --- But if you just started your course in Computer Science, then I will give you some “bookshelf advice" based on my experience. I had the pleasure to study all the books I am going to recommend you, and most of them I was able to read cover-to-cover during the university years. And they are also in my bookshelf for reference. The book order does not represent rank of importance. * “Introduction to the Theory of Computation”, by Michael Sipser. * I also recommend the “Elements of the Theory of Computation”, by Christos Papadimitriou. * Another good complement is “Introduction to Automata Theory, Languages and Computation”, by Hopcroft and Ullman. (Thanks, @reacweb, for the reminder.) * “Graph Theory”, by Reinhard Diestel.…